A monk's Deflect Missiles ability (PHB p. 78) triggers on the following circumstance:
Starting at 3rd level, you can use your reaction to deflect or catch the missile when you are hit by a ranged weapon attack.
Does this work against thrown melee weapons, such as a javelin or dagger?
The Sage Advice Compendium has clarified what is meant by "ranged weapon attack" (italics added).
What does “melee weapon attack” mean: a melee attack with a weapon or an attack with a melee weapon? It means a melee attack with a weapon. Similarly, “ranged weapon attack” means a ranged attack with a weapon.
If you throw a melee weapon, you are making a ranged attack, and you are using a weapon. Thus, you are making a "ranged weapon attack." Therefore, the attack is a valid one for a monk to attempt to "deflect".
Note that this definition applies even if the weapon in question doesn't have the "thrown" property (although it would then be counted as an "improvised weapon", it's still a weapon that is being used to make a ranged attack.)
From the Equipment chapter of the Basic Rules.
Thrown. If a weapon has the thrown property, you can throw the weapon to make a ranged attack.
The attack is a ranged attack using a weapon, which is a "ranged weapon attack"¹, so the Monk feature applies.
If someone throws an item that is not a weapon with the thrown tag then it is an improvised weapon. You are still making an attack roll, so it is a ranged weapon attack. (Hat-tip @Rubiksmoose.)
An object that bears no resemblance to a weapon deals 1d4 damage (the DM assigns a damage type appropriate to the object). If a character uses a ranged weapon to make a melee attack, or throws a melee weapon that does not have the thrown property, it also deals 1d4 damage. An improvised thrown weapon has a normal range of 20 feet and a long range of 60 feet.
¹ The Equipment chapter does not use the phrase "ranged weapon attack" but the Combat chapter does, though only twice (one of which is in the Underwater Combat section).
Ability Modifier. The ability modifier used for a melee weapon attack is Strength, and the ability modifier used for a ranged weapon attack is Dexterity. Weapons that have the finesse or thrown property break this rule.
